So far as I can tell, the Salem (Mass) births were published in book form in 1916, but sorted alphabetically. Bad idea - you lose the original order of the records as a check against ambiguities, mistakes and mistranscriptions in the dates.
On the face of it, I'd take 1: 3mo: 1642 to mean 1st May 1642, and 13: 1: 1642 to mean 13 Mar 1642/3, 10 months later.
Perley gave the baptisms of Elder John Browne's kids in 1909 (before the register was printed). Perley's dates match the book.
https://archive.org/details/essexantiquaria06perlgoog/page/n1645
Those two dates appear, but the other way round. Either Perley has somehow got them in the wrong order, or else, if the order is as they came, the numbers have to be interpreted differently.
Can anybody shed any light?